1 Answer

Toolbox:

Equation of a straight line passing through a given point and parallel to a given vector $ \overrightarrow r = \overrightarrow a+t\overrightarrow v$ ( vector equation ) where $\overrightarrow a$ is the pv of the point and $ \overrightarrow v$ the vector parallel to the line, a scalar $ \large\frac{x-x_1}{l} = \large\frac{y-y_1}{m} = \large\frac{z-z_1}{n}$ ( cartesian form) where $(x_1, y_1, z_1) $ is the point on the line and $ l, m, n$ are the d.c.s of the vector parallel to the line $ l, m, n$ can also be replaced by the d.r.s $ a, b, c$.